Bob is building a wooden cabin. The cabin is $30$ meters wide. He obtained a bunch of $17$ meters long wooden beams for the roof of the cabin. Naturally, he wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams? Round your final answer to the nearest tenth.
Explanation: The strategy Model the situation as a right triangle. Determine the appropriate trigonometric ratio in order to find the missing angle. Form an equation and solve for the missing angle. Calculate the final result and round. Modeling as a right triangle This situation can be modeled by the following right triangle. The hypotenuse is $17\text{ m}$ and the base is half of $30\text{ m}$, which is $15\text{ m}$. We are asked to find the angle of elevation of the roof beams, which is the angle on the right. $?$ $17$ $15$ Determining the appropriate trigonometric ratio We are given the side ${\text{adjacent}}$ to the missing angle and the $C{\text{hypotenuse}}$. The appropriate trigonometric ratio is therefore the $\text{cosine}$. Forming an equation and solving Denoting the missing angle by $\theta$, we obtain the equation $\cos(\theta)=\dfrac{15}{17}$. Solving the equation, we get $\theta=\cos^{-1}\left(\dfrac{15}{17}\right)$. Evaluating this result in the calculator and rounding to the nearest tenth, we get $\theta=28.1^\circ$. Summary The angle of elevation of the roof beams is $28.1^\circ$.